First we provide a brief review of the existing literature
on the detection of multiple change points in stochastic properties other than the mean,
in univariate or multivariate data sequences.
Under parametric models for linear and non-linear time series,
\(\ell _0\) - [1]}, [2]}, [3]} and
\(\ell _1\) -penalisation [4]} methods,
the MOSUM procedure based on likelihood ratio statistic [5]}
and BS [6]}
have been adopted for detecting change points in
the parameters that vary over time in a piecewise constant manner.
The problems of multiple change point detection
under piecewise polynomial (mostly linear) models
have been addressed in [7]}, [8]}, [9]}, [10]},
also adopting the data segmentation algorithms discussed in Section .
For nonparametric change point analysis,
BS [11]}, WBS [12]} and
\(\ell _0\) -penalisation [13]}, [14]}
have been combined with various methods for measuring distributional changes,
and some computational efforts have been made
to improve the dynamic programming algorithms
for the methods in the latter category [15]}, [16]}.
In the time series setting, methods based on local periodograms [17]}
and wavelet transform [18]} have been developed
in combination with the MOSUM procedure and BS, respectively.
